four more than twice a number is greater than negative eighteen. Solve the inequality for the unknown number

A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. The number of subjects needed to estima

Ludmilka [50]

Answer:

$n=(\frac{1.64(14.7)}{3})^2 =64.57 \approx 65$

So the answer for this case would be n=65 rounded up to the nearest integer

And the sample size would decrease by 160-65=95 subjects

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

ME represent the margin of error

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

2) Solution to the problem

Since the new Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Assuming that the deviation is known we can express the margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =\pm 3 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

Replacing into formula (b) we got:

$n=(\frac{1.64(14.7)}{3})^2 =64.57 \approx 65$

So the answer for this case would be n=65 rounded up to the nearest integer

And the sample size would decrease by 160-65=95 subjects

8 0

3 years ago

Please help me ASAP! I will friend you (probably)! The first correct answer will get brainiest! Terry and Tao are canoeing on a

ivann1987 [24]

erry starts rowing at 2 pm from the west end of the lake, and Tao starts rowing from the east end of the lake at 2:05 pm.
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Terry DATA:
rate = 60 meter/min ; time = x min ; distance = r*t = 60x meters
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Tao DATA:
rate = 40 meter/min ; time = x-5 min ; distance = r*t = 40(x-5) meters
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If they always row directly towards each other at what time will the two meet?

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Equation:
dist + dist = 2000 meters
60x + 40(x-5) = 2000
20x = 1800
x = 90 minutes
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8 0

3 years ago

K is the midpoint of JL. JK = 2x + 5 and JL = 50.

Sergeu [11.5K]

Steve set the equation equal to 50 which is the entire length of JL. instead he should've set the equation equal to 25, since it's half of 50 and would represent the midpoint. he should've said 2x + 5 = 25

8 0

3 years ago

Which graph shows a dilation?

dimulka [17.4K]

Answer:

The third one.

Explanation:

A dilation is a shrink or a stretch of a figure.

In a dilation, all sides either increase or decrease by the same scale factor. Additionally, in a dilation the angle measures of the figure do not change.

In the first figure, we can see that the base angles of the pre-image are slightly different than those of the image. This is not a dilation.

In the second figure, the angles are noticeably different; again, not a dilation.

In the fourth figure, much like the second figure, the angles are noticeably different. This is not a dilation.

In the third figure, however, we can see that the slanted sides of the larger figure go through three boxes; they are three units long. Additionally we can see that the slanted sides of the smaller figure go through 1 side; this is a dilation b a factor of 3.

The base sides of the third figure, in the larger shape, are 6 units long; in the smaller figure, they are 2 units long. This is a dilation by a factor of 3.

6 0

3 years ago

Read 2 more answers

What is the best estimate of 49% of 598

Maslowich

49% of 598 = 598*49/100 = 293.02

4 0

3 years ago

Read 2 more answers